Answer
$\left[ 6,\infty \right)$
Work Step by Step
Solving the inequalities separately, then,
\begin{array}{l}
x+1\ge7\\
x\ge6
,\\\\\text{and}\\\\
3x-1\ge5\\
3x\ge6\\
x\ge2
.\end{array}
Using the conjunction "and", then the solution set is the set common to both inequalities. Hence, the solution set is $
\left[ 6,\infty \right)
$.